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Observational ultraproducts of polynomial coalgebras

Robert Goldblatt
2003 Annals of Pure and Applied Logic  
doi:10.1016/s0168-0072(03)00038-1 fatcat:5icjz4t7xragxmsam7jwmjh5qm

Ultraproducts of Tannakian Categories and Generic Representation Theory of Unipotent Algebraic Groups [article]

Michael Crumley
2010 arXiv   pre-print
, ultraproducts of them.  ...  One of the main theorems of this dissertation is that certain naturally definable subcategories of these ultraproducts are themselves neutral tannakian categories, hence tensorially equivalent to Comod_A  ...  The representing Hopf algebra of the restricted ultraproduct R Comod A i is coalgebra-isomorphic to the restricted ultraproduct A R of the Hopf algebras A i .Proof.  ... 
arXiv:1011.0460v1 fatcat:egfuzgtem5ewbfhx3dldm2elsi

6 Algebras and coalgebras [chapter]

Yde Venema
2007 Studies in Logic and Practical Reasoning  
In the second and last part of the chapter we describe how modal logic, and its model theory, provides many natural manifestations of the more general theory of universal coalgebra. 1 This text has been  ...  This chapter 1 sketches some of the mathematical surroundings of modal logic.  ...  Acknowledgments Many people have contributed to this chapter by commenting on earlier versions of it.  ... 
doi:10.1016/s1570-2464(07)80009-7 fatcat:e77uebqxdferlcg2nlfe5hobpq

A comonadic account of behavioural covarieties of coalgebras

ROBERT GOLDBLATT
2005 Mathematical Structures in Computer Science  
K may be thought of as the class of all coalgebras that satisfy some computationally significant property.  ...  We show that there is a bijective correspondence between behavioural covarieties of T -coalgebras and isomorphism classes of pure subcomonads of G T .  ...  of observational ultrapowers of polynomial coalgebras in (Goldblatt, 2003c) .  ... 
doi:10.1017/s096012950400458x fatcat:g5aflvvy4rbkhoa45l7d3dnina

Probabilistic logics based on Riesz spaces

Robert Furber, Radu Mardare, Matteo Mio
2019 Logical Methods in Computer Science  
By using powerful results from this theory, we develop the duality theory of the Riesz modal logic in the form of an algebra-to-coalgebra correspondence.  ...  The design of the syntax and semantics of this logic is directly inspired by the theory of Riesz spaces, a mature field of mathematics at the intersection of universal algebra and functional analysis.  ...  Acknowledgements The work of Mio has been partially supported by the French project ANR-16-CE25-0011 REPAS.  ... 
doi:10.23638/lmcs-16(1:6)2020 fatcat:vqm3un3yqfbs3nckws4dnqqzpu

Probabilistic logics based on Riesz spaces [article]

Robert Furber and Radu Mardare and Matteo Mio
2020 arXiv   pre-print
By using powerful results from this theory, we develop the duality theory of the Riesz modal logic in the form of an algebra-to-coalgebra correspondence.  ...  The design of the syntax and semantics of this logic is directly inspired by the theory of Riesz spaces, a mature field of mathematics at the intersection of universal algebra and functional analysis.  ...  Acknowledgements The work of Mio has been partially supported by the French project ANR-16-CE25-0011 REPAS.  ... 
arXiv:1903.09463v3 fatcat:pqk4bz4hiffxbklkm33ovkrehe

Cocommutative coalgebras: homotopy theory and Koszul duality

Joseph Chuang, Andrey Lazarev, W. H. Mannan
2016 Homology, Homotopy and Applications  
We extend a construction of Hinich to obtain a closed model category structure on all differential graded cocommutative coalgebras over an algebraically closed field of characteristic zero.  ...  We further show that the Koszul duality between commutative and Lie algebras extends to a Quillen equivalence between cocommutative coalgebras and formal coproducts of curved Lie algebras.  ...  dg coalgebras over a field of characteristic zero.  ... 
doi:10.4310/hha.2016.v18.n2.a17 fatcat:p5kkrcak2vaorppexqryf5kigm

Cocommutative coalgebras: homotopy theory and Koszul duality [article]

J. Chuang, A. Lazarev, W.H. Mannan
2014 arXiv   pre-print
We extend a construction of Hinich to obtain a closed model category structure on all differential graded cocommutative coalgebras over an algebraically closed field of characteristic zero.  ...  We further show that the Koszul duality between commutative and Lie algebras extends to a Quillen equivalence between cocommutative coalgebras and formal coproducts of curved Lie algebras.  ...  dg coalgebras over a field of characteristic zero.  ... 
arXiv:1403.0774v1 fatcat:bhxlr4xnk5grdd3qcqmz6aqizm

Metamathematics for Systems Design

Ichiro Hasuo
2017 New generation computing  
However, there are fundamental gaps in application of formal methods to industry products: additional concerns in industry products such as continuous dynamics of physical components and quantitative measures  ...  This position paper describes the context, the goal, the strategy and the tactics of the ERATO MMSD project (2016-2022.  ...  Acknowledgements Thanks are due to the following people: the core members of the ERATO MMSD project (Krzysztof Czarnecki, Masahito Hasegawa, Fuyuki Ishikawa, Shin-ya Katsumata, Kohei Suenaga, Toshimitsu  ... 
doi:10.1007/s00354-017-0023-1 fatcat:pw6byl77njf2boltl4qbjdh3ba

Page 852 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
(Natalia Bebiano) 2004d:15010 15A15 (15A48) Goldblatt, Robert Observational ultraproducts of polynomial coalgebras. (English summary) Ann. Pure Appl. Logic 123 (2003), no. 1-3, 235-290.  ...  The Sylvester resultant matrix for Bernstein polynomials. (English summary) Curve and surface design (Saint-Malo, 2002), 407-416, Mod. Methods Math., Nashboro Press, Brentwood, TN, 2003.  ... 

Fourier's Method of Linear Programming and Its Dual

H. P. Williams
1986 The American mathematical monthly  
systems, model-matching, etc.) 93A99 None of the above, but in this section 93Bxx Controllability, observability, and system structure 93B03 Attainable sets 93B05 Controllability 93B07 Observability  ...  of functions 26B99 None of the above, but in this section 26Cxx Polynomials, rational functions 26C05 Polynomials: analytic properties, etc.  ...  Observational and experimental questions 83B05 Observational and experimental questions 83B99 None of the above, but in this section 83Cxx General relativity 83C05 Einstein's equations (general structure  ... 
doi:10.2307/2322281 fatcat:yvhgyh2epbcwdoqdhuaopkcrue

On the Frobenius functor for symmetric tensor categories in positive characteristic [article]

Pavel Etingof, Victor Ostrik
2020 arXiv   pre-print
We develop a theory of Frobenius functors for symmetric tensor categories (STC) C over a field k of characteristic p, and give its applications to classification of such categories.  ...  We also show that a sufficiently large power of F lands in C_ ex.  ...  The work of P. E. was partially supported by the NSF grant DMS-1502244. The work of V.  ... 
arXiv:1912.12947v2 fatcat:d5ztonbzg5ap3k6ovfxenrsnvm

Definable additive categories: purity and model theory

Mike Prest
2011 Memoirs of the American Mathematical Society  
In particular, if F commutes with ultraproducts (meaning, commutes with those ultraproducts of pureinjective objects of D which are themselves pure-injective) then (F p /F ψ ) D must be a finitely generated  ...  We consider a functor from Mod-k[T ] to Mod-k A 1 , where k is a field, k[T ] is the polynomial ring and k A 1 is the path algebra of the Kronecker quiver A 1 .  ... 
doi:10.1090/s0065-9266-2010-00593-3 fatcat:a5cgsl5w5bgpfidsdqb4jcw5qi

Complete Additivity and Modal Incompleteness [article]

Wesley H. Holliday, Tadeusz Litak
2018 arXiv   pre-print
On the other hand, we observe that it is undecidable whether a syntactically defined logic is V-complete. After these results, we generalize the Blok Dichotomy to degrees of V-incompleteness.  ...  In the end, we return to van Benthem's theme of syntactic aspects of modal incompleteness.  ...  This by itself does not lead to "natural" examples of coalgebraic logics where mild rules like our V-mod are inadmissible; coalgebraic logicians focus almost exclusively on minimal logics, axiomatizable  ... 
arXiv:1809.07542v1 fatcat:priuo4blnjhozdoajxxfyy6f6y

Extending torsors on the punctured Spec(A_inf) [article]

Johannes Anschütz
2020 arXiv   pre-print
As applications we extend results of Ivanov on exactness of the loop functor and present the construction of a canonical specialization map from the B^+_dR-affine Grassmannian to the Witt vector affine  ...  Using descent we can extend a similar result for the ring 𝔖 of Kisin and Pappas to full generality. Moreover, we treat similarly the case of equal characteristic.  ...  This equivalence respects tensor products and hence induces an equivalence on algebra/coalgebra objects.  ... 
arXiv:1804.06356v2 fatcat:m7ydzra565fybc4rg57oxezbiy
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